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    The line with equation y=mx-2 meets the ellipse with equation x²+4y²=16 at the points P and Q.

    a) Find the midpoint M of P and Q, giving each co ordinate in terms of m,
    x=16m/(1+4m2)
    y=-2/(1+4m2)

    b) As m varies, find in cartesian form, an equation of the locus of M
    Stuck on this one.
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    (Original post by bobbricks)
    The line with equation y=mx-2 meets the ellipse with equation x²+4y²=16 at the points P and Q.

    a) Find the midpoint M of P and Q, giving each co ordinate in terms of m,
    x=16m/(1+4m2)
    y=-2/(1+4m2)
    I get x= \frac{8m}{1+4m^2} so one of us seems to be a factor of 2 out. I agree with the expression for y

    b) As m varies, find in cartesian form, an equation of the locus of M
    Stuck on this one.
    You have to eliminate m between the expressions that you have for x,y to find an equation for the locus in terms of x,y.
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    (Original post by bobbricks)
    The line with equation y=mx-2 meets the ellipse with equation x²+4y²=16 at the points P and Q.

    a) Find the midpoint M of P and Q, giving each co ordinate in terms of m,
    x=16m/(1+4m2)
    y=-2/(1+4m2)

    b) As m varies, find in cartesian form, an equation of the locus of M
    Stuck on this one.
    As you see from the coordinates of the M

    x=-8m*y -> y= ...... gives the equation of the locus of M (which will be a line)
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    (Original post by ztibor)
    As you see from the coordinates of the M

    x=-8m*y -> y= ...... gives the equation of the locus of M (which will be a line)
    Which line? I get an ellipse.
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    Okay, thanks guys! I've managed to get an equation of an ellipse though (which seems to be the correct answer)
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    (Original post by ztibor)
    As you see from the coordinates of the M

    x=-8m*y -> y= ...... gives the equation of the locus of M (which will be a line)

    (Original post by atsruser)
    Which line? I get an ellipse.
    May I join in?

    I have not done it but I expect an ellipse.

    If the parametrics are correct divide the equations to get m = -x/(8y) and substitute into the easier equation
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    (Original post by atsruser)
    I get x= \frac{8m}{1+4m^2} so one of us seems to be a factor of 2 out. I agree with the expression for y



    You have to eliminate m between the expressions that you have for x,y to find an equation for the locus in terms of x,y.
    Your value for x is correct
 
 
 
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